scholarly journals Drops with insoluble surfactant squeezing through interparticle constrictions

2019 ◽  
Vol 878 ◽  
pp. 324-355 ◽  
Author(s):  
Jacob R. Gissinger ◽  
Alexander Z. Zinchenko ◽  
Robert H. Davis
Keyword(s):  
Surface Tension ◽  
Capillary Number ◽  
Surfactant Concentration ◽  
Boundary Integral ◽  
Interfacial Stress ◽  
Multiphase System ◽  
Concentration Gradients ◽  
Surfactant Transport ◽  
Critical Capillary Number ◽  
Medium Viscosity

The interfacial behaviour of surfactant-laden drops squeezing through tight constrictions in a uniform far-field flow is modelled with respect to capillary number, drop-to-medium viscosity ratio and surfactant contamination. The surfactant is treated as insoluble and non-diffusive, and drop surface tension is related to surfactant concentration by a linear equation of state. The constriction is formed by three solid spheres held rigidly in space. A characteristic aspect of this confined and contaminated multiphase system is the rapid development of steep surfactant-concentration gradients during the onset of drop squeezing. The interplay between two physical effects of surfactant, namely the greater interface deformability due to decreased surface tension and interface immobilization due to Marangoni stresses, results in particularly rich drop-squeezing dynamics. A three-dimensional boundary-integral algorithm is used to describe drop hydrodynamics, and accurate treatment of close squeezing and trapped states is enabled by advanced singularity subtraction techniques. Surfactant transport and hydrodynamics are coupled via the surface convection equation (or convection–diffusion equation, if artificial diffusion is included), the interfacial stress balance and a solid-particle contribution based on the Hebeker representation. For extreme conditions, such as drop-to-medium viscosity ratios significantly less than unity, it is found that upwind-biased methods are the only stable approaches for modelling surfactant transport. Two distinct schemes, upwind finite volume and flow-biased least squares, are found to provide results in close agreement, indicating negligible numerical diffusion. Surfactant transport is enhanced by low drop-to-medium viscosity ratios, at which extremely sharp concentration gradients form during various stages of the squeezing process. The presence of surfactant, even at low degrees of contamination, significantly decreases the critical capillary number for droplet trapping, due to the accumulation of surfactant at the downwind pole of the drop and its subsequent elongation. Increasing the degree of contamination significantly affects surface mobility and further decreases the critical capillary number as well as drop squeezing times, up to a threshold above which the addition of surfactant negligibly affects squeezing dynamics.

Instability of two-layer creeping flow in a channel with parallel-sided walls

1997 ◽  
Vol 351 ◽  
pp. 139-165 ◽  
Author(s):  
C. POZRIKIDIS
Keyword(s):  
Surface Tension ◽  
Reynolds Number ◽  
Stokes Flow ◽  
Capillary Number ◽  
Travelling Waves ◽  
Boundary Integral ◽  
Creeping Flow ◽  
Two Dimensional ◽  
Two Fluids ◽  
Axial Pressure Gradient

The evolution of the interface between two viscous fluid layers in a two-dimensional horizontal channel confined between two parallel walls is considered in the limit of Stokes flow. The motion is generated either by the translation of the walls, in a shear-driven or plane-Couette mode, or by an axial pressure gradient, in a plane-Poiseuille mode. Linear stability analysis for infinitesimal perturbations and fluids with matched densities shows that when the viscosities of the fluids are different and the Reynolds number is sufficiently high, the flow is unstable. At vanishing Reynolds number, the flow is stable when the surface tension has a non-zero value, and neutrally stable when the surface tension vanishes. We investigate the behaviour of the interface subject to finite-amplitude two-dimensional perturbations by solving the equations of Stokes flow using a boundary-integral method. Integral equations for the interfacial velocity are formulated for the three modular cases of shear-driven, pressure-driven, and gravity-driven flow, and numerical computations are performed for the first two modes. The results show that disturbances of sufficiently large amplitude may cause permanent interfacial deformation in which the interface folds, develops elongated fingers, or supports slowly evolving travelling waves. Smaller amplitude disturbances decay, sometimes after a transient period of interfacial folding. The ratio of the viscosities of the two fluids plays an important role in determining the morphology of the emerging interfacial patterns, but the parabolicity of the unperturbed velocity profile does not affect the character of the motion. Increasing the contrast in the viscosities of the two fluids, while keeping the channel capillary number fixed, destabilizes the interfaces; re-examining the flow in terms of an alternative capillary number that is defined with respect to the velocity drop across the more-viscous layer shows that this is a reasonable behaviour. Comparing the numerical results with the predictions of a lubrication-flow model shows that, in the absence of inertia, the simplified approach can only describe a limited range of motions, and that the physical relevance of the steadily travelling waves predicted by long-wave theories must be accepted with a certain degree of reservation.

The effect of surfactants on drop deformation and on the rheology of dilute emulsions in Stokes flow

1997 ◽  
Vol 341 ◽  
pp. 165-194 ◽  
Author(s):  
XIAOFAN LI ◽  
C. POZRIKIDIS
Keyword(s):  
Surface Tension ◽  
Stokes Flow ◽  
Capillary Number ◽  
Surfactant Concentration ◽  
Drop Deformation ◽  
Main Body ◽  
Incident Flow ◽  
Spherical Drop ◽  
Convection Diffusion ◽  
Elasticity Number

The effect of an insoluble surfactant on the transient deformation and asymptotic shape of a spherical drop that is subjected to a linear shear or extensional flow at vanishing Reynolds number is studied using a numerical method. The viscosity of the drop is equal to that of the ambient fluid, and the interfacial tension is assumed to depend linearly on the local surfactant concentration. The drop deformation is affected by non-uniformities in the surface tension due to the surfactant molecules convection–diffusion. The numerical procedure combines the boundary-integral method for solving the equations of Stokes flow, and a finite-difference method for solving the unsteady convection–diffusion equation for the surfactant concentration over the evolving interface. The parametric investigations address the effect of the ratio of the vorticity to the rate of strain of the incident flow, the Péclet number expressing the ability of the surfactant to diffuse, the elasticity number expressing the sensitivity of the surface tension to variations in surfactant concentration, and the capillary number expressing the strength of the incident flow. At small and moderate capillary numbers, the effect of a surfactant in a non-axisymmetric flow is found to be similar to that in axisymmetric straining flow studied by previous authors. The accumulation of surfactant molecules at the tips of an elongated drop decreases the surface tension locally and promotes the deformation, whereas the dilution of the surfactant over the main body of the drop increases the surface tension and restrains the deformation. At large capillary numbers, the dilution of the surfactant and the rotational motion associated with the vorticity of the incident flow work synergistically to increase the critical capillary number beyond which the drop exhibits continuous elongation. The numerical results establish the regions of validity of the small-deformation theory developed by previous authors, and illustrate the influence of the surfactant on the flow kinematics and on the rheological properties of a dilute suspension. Surfactants have a stronger effect on the rheology of a suspension than on the deformation of the individual drops.

General rheology of highly concentrated emulsions with insoluble surfactant

2017 ◽  
Vol 816 ◽  
pp. 661-704 ◽  
Author(s):  
Alexander Z. Zinchenko ◽  
Robert H. Davis
Keyword(s):  
Surfactant Concentration ◽  
Large Scale ◽  
Boundary Integral ◽  
Base Flow ◽  
Interfacial Stress ◽  
Time Dependent ◽  
Carrier Fluid ◽  
Insoluble Surfactant ◽  
Long Time ◽  
Base Flows

A general constitutive model is constructed and validated for highly concentrated monodisperse emulsions of deformable drops with insoluble surfactant through long-time, large-scale and high-resolution multidrop simulations. There is the same amount of surfactant on each drop, and the linear model is assumed for the surface tension versus the surfactant concentration. The surfactant surface transport is coupled to multidrop hydrodynamics through the convective–diffusive equation and the interfacial stress balance. Only the limit of small surfactant diffusivities is addressed, when this parameter does not affect the rheology. An Oldroyd constitutive equation is postulated, with five variable coefficients depending on one instantaneous flow invariant (chosen as the drop-phase contribution to the dissipation rate). These coefficients are found by fitting the model to five precise rheological functions from two steady base flows at arbitrary deformation rates. One base flow is planar extension (PE) ($\dot{\unicode[STIX]{x1D6E4}}x_{1},-\dot{\unicode[STIX]{x1D6E4}}x_{2},0$), the other one is planar mixed flow (PM) ($\dot{\unicode[STIX]{x1D6FE}}x_{2}$, $\dot{\unicode[STIX]{x1D6FE}}\unicode[STIX]{x1D712}x_{1}$, 0) with $\unicode[STIX]{x1D712}=0.16$. A small but finite $\unicode[STIX]{x1D712}$ (a precise choice in the range $\unicode[STIX]{x1D712}\sim 0.1$ is unimportant) provides a necessarily perturbation to exclude severe ergodic difficulties and abnormal, kinked behaviour inherent in simple shear for high drop volume fractions $c$, especially at small capillary numbers $Ca$ and small drop-to-medium viscosity ratios $\unicode[STIX]{x1D706}$. The database rheological functions are obtained for $c=0.45{-}0.6$, $\unicode[STIX]{x1D706}=0.25{-}3$ and surfactant elasticities $\unicode[STIX]{x1D6FD}=0.05{-}0.2$ (based on the equilibrium surfactant concentration) from long-time simulations by a multipole-accelerated boundary-integral code with $N=100{-}200$ drops in a periodic cell and 2000–4000 boundary elements per drop. The code is an extension from Zinchenko & Davis (J. Fluid Mech., vol. 779, 2015, pp. 197–244) to account for surfactant transport and Marangoni stresses. Massive drop cusping or (sometimes) drop break-up limit the range of $Ca$ from above in the base flows, but there is no substantial lower limitation owing to the absence of phase transition difficulties. At small $\unicode[STIX]{x1D706}$, even minimal surface contamination may have a strong effect on the rheology. The simulations remain accurate for quite strong drop interactions, when the PE emulsion viscosity is nine times that for the carrier fluid. The model validation against a steady PM flow with a different $\unicode[STIX]{x1D712}=0.5$ shows a very good agreement for various $Ca$, $c$ and $\unicode[STIX]{x1D706}$. In the three PE and PM time-dependent flow tests, the quasi-steady approximation is found to predict stresses poorly. In contrast, the combination of the steady-state results for PE and PM used in the present method to generate the Oldroyd parameters gives a model with much better predictions for these time-dependent flows.

The role of surface charge convection in the electrohydrodynamics and breakup of prolate drops

2017 ◽  
Vol 833 ◽  
pp. 29-53 ◽  
Author(s):  
Rajarshi Sengupta ◽  
Lynn M. Walker ◽  
Aditya S. Khair
Keyword(s):  
Surface Charge ◽  
Capillary Number ◽  
Boundary Integral ◽  
Drop Deformation ◽  
Number Ratio ◽  
Dc Electric Field ◽  
Weakly Conducting ◽  
Critical Capillary Number ◽  
Breakup Mode

The deformation of a weakly conducting, ‘leaky dielectric’, drop in a density matched, immiscible weakly conducting medium under a uniform direct current (DC) electric field is quantified computationally. We exclusively consider prolate drops, for which the drop elongates in the direction of the applied field. Furthermore, for the majority of this study, we assume the drop and medium to have equal viscosities. Using axisymmetric boundary integral computations, we delineate drop deformation and breakup regimes in the $Ca_{E}-Re_{E}$ parameter space, where $Ca_{E}$ is the electric capillary number (ratio of the electric to capillary stresses); and $Re_{E}$ is the electric Reynolds number (ratio of charge relaxation to flow time scales), which characterizes the strength of surface charge convection along the interface. For so-called ‘prolate A’ drops, where the surface charge is convected towards the ‘poles’ of the drop, we demonstrate that increasing $Re_{E}$ reduces the critical capillary number for breakup. Moreover, surface charge convection is the cause of an abrupt transition in the breakup mode of a drop from end pinching, where the drop elongates and develops bulbs at its ends that eventually detach, to a breakup mode characterized by the formation of conical ends. On the contrary, the deformation of ‘prolate B’ drops, where the surface charge is convected away from the poles, is essentially unaffected by the magnitude of $Re_{E}$.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

Influence of pressure-dependent surface viscosity on dynamics of surfactant-laden drops in shear flow

2018 ◽  
Vol 858 ◽  
pp. 91-121 ◽  
Author(s):  
Zheng Yuan Luo ◽  
Xing Long Shang ◽  
Bo Feng Bai
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Surfactant Concentration ◽  
Constitutive Law ◽  
Simple Shear Flow ◽  
Drop Surface ◽  
Shear Surface ◽  
Surface Viscosity ◽  
Principal Axes ◽  
Surfactant Transport

We study numerically the dynamics of an insoluble surfactant-laden droplet in a simple shear flow taking surface viscosity into account. The rheology of drop surface is modelled via a Boussinesq–Scriven constitutive law with both surface tension and surface viscosity depending strongly on the surface concentration of the surfactant. Our results show that the surface viscosity exhibits non-trivial effects on the surfactant transport on the deforming drop surface. Specifically, both dilatational and shear surface viscosity tend to eliminate the non-uniformity of surfactant concentration over the drop surface. However, their underlying mechanisms are entirely different; that is, the shear surface viscosity inhibits local convection due to its suppression on drop surface motion, while the dilatational surface viscosity inhibits local dilution due to its suppression on local surface dilatation. By comparing with previous studies of droplets with surface viscosity but with no surfactant transport, we find that the coupling between surface viscosity and surfactant transport induces non-negligible deviations in the dynamics of the whole droplet. More particularly, we demonstrate that the dependence of surface viscosity on local surfactant concentration has remarkable influences on the drop deformation. Besides, we analyse the full three-dimensional shape of surfactant-laden droplets in simple shear flow and observe that the drop shape can be approximated as an ellipsoid. More importantly, this ellipsoidal shape can be described by a standard ellipsoidal equation with only one unknown owing to the finding of an unexpected relationship among the drop’s three principal axes. Moreover, this relationship remains the same for both clean and surfactant-laden droplets with or without surface viscosity.

Surface Activity Research of Cationic Gemini Surfactants

2013 ◽  
Vol 690-693 ◽  
pp. 2076-2080
Author(s):  
Zhen Zhong Fan ◽  
Lan Lan Li ◽  
Li Feng Zhang ◽  
Qing Wang Liu
Keyword(s):  
Surface Tension ◽  
Critical Micelle Concentration ◽  
Surface Activity ◽  
Surfactant Concentration ◽  
Gemini Surfactant ◽  
Gemini Surfactants ◽  
Ph Value ◽  
Inorganic Salts ◽  
Cationic Gemini Surfactant ◽  
Cationic Gemini Surfactants

Cationic Gemini surfactant concentration, the inorganic salts added and the pH value of surface tension obtained cationic gemini surfactant critical micelle concentration is 0.4mmol / L;by adding three kinds of inorganic salts NaCl, MgCl2, and Na2SO4 ,which Na2SO4 has the greatest impact on surface tension, followed by MgCl2.The surface minimum tension of the pH ranged from 9 to 11 , indicating that the surface activity of cationic gemini surfactants achieved the highest.

scholarly journals Drop deformation by laser-pulse impact

2016 ◽  
Vol 794 ◽  
pp. 676-699 ◽  
Author(s):  
Hanneke Gelderblom ◽  
Henri Lhuissier ◽  
Alexander L. Klein ◽  
Wilco Bouwhuis ◽  
Detlef Lohse ◽  
...  
Keyword(s):  
Surface Tension ◽  
Laser Pulse ◽  
Time Scale ◽  
Pulse Shape ◽  
Thin Sheet ◽  
Boundary Integral ◽  
Drop Deformation ◽  
Nanosecond Laser Pulse ◽  
Nanosecond Laser ◽  
Energy Partition

A free falling, absorbing liquid drop hit by a nanosecond laser pulse experiences a strong recoil pressure kick. As a consequence, the drop propels forward and deforms into a thin sheet which eventually fragments. We study how the drop deformation depends on the pulse shape and drop properties. We first derive the velocity field inside the drop on the time scale of the pressure pulse, when the drop is still spherical. This yields the kinetic energy partition inside the drop, which precisely measures the deformation rate with respect to the propulsion rate, before surface tension comes into play. On the time scale where surface tension is important, the drop has evolved into a thin sheet. Its expansion dynamics is described with a slender-slope model, which uses the impulsive energy partition as an initial condition. Completed with boundary integral simulations, this two-stage model explains the entire drop dynamics and its dependence on the pulse shape: for a given propulsion, a tightly focused pulse results in a thin curved sheet which maximizes the lateral expansion, while a uniform illumination yields a smaller expansion but a flat symmetric sheet, in good agreement with experimental observations.

Effect of surfactants on capacitance properties of carbon electrodes

2011 ◽  
Vol 1333 ◽  
Author(s):  
Krzysztof Fic ◽  
Grzegorz Lota ◽  
Elzbieta Frackowiak
Keyword(s):  
Surface Tension ◽  
Alkaline Solution ◽  
Surfactant Concentration ◽  
Alkaline Solutions ◽  
Carbon Electrodes ◽  
Current Load ◽  
Target Concentration ◽  
Electrolyte Additives ◽  
Different Types ◽  
Triton X

ABSTRACTEffect of surfactants present in alkaline solutions on the capacitance of carbon electrodes has been studied. Different types of surfactants have been selected for this target. Concentration of these electrolyte additives was 0.005 mol L-1. Decreasing the surface tension in the electrode/electrolyte interface allows better penetration of electrolyte into the pores. Detailed analysis of capacitance versus current load, frequency dependence as well as self-discharge, cyclability and behaviour in wider voltage window proved a useful effect of Triton X-100 on capacitor operating in alkaline solution. Influence of surfactant concentration has also been investigated.

Effect of Gravity on Liquid Plug Transport Through an Airway Bifurcation Model

2005 ◽  
Vol 127 (5) ◽  
pp. 798-806 ◽  
Author(s):  
Y. Zheng ◽  
J. C. Anderson ◽  
V. Suresh ◽  
J. B. Grotberg
Keyword(s):  
Capillary Number ◽  
Axial Direction ◽  
Bond Number ◽  
Liquid Volume ◽  
Liquid Plug ◽  
Splitting Ratio ◽  
Wide Range ◽  
Critical Capillary Number ◽  
Airway Bifurcation ◽  
Parent Tube

Many medical therapies require liquid plugs to be instilled into and delivered throughout the pulmonary airways. Improving these treatments requires a better understanding of how liquid distributes throughout these airways. In this study, gravitational and surface mechanisms determining the distribution of instilled liquids are examined experimentally using a bench-top model of a symmetrically bifurcating airway. A liquid plug was instilled into the parent tube and driven through the bifurcation by a syringe pump. The effect of gravity was adjusted by changing the roll angle (ϕ) and pitch angle (γ) of the bifurcation (ϕ=γ=0deg was isogravitational). ϕ determines the relative gravitational orientation of the two daughter tubes: when ϕ≠0deg, one daughter tube was lower (gravitationally favored) compared to the other. γ determines the component of gravity acting along the axial direction of the parent tube: when γ≠0deg, a nonzero component of gravity acts along the axial direction of the parent tube. A splitting ratio Rs, is defined as the ratio of the liquid volume in the upper daughter to the lower just after plug splitting. We measured the splitting ratio, Rs, as a function of: the parent-tube capillary number (Cap); the Bond number (Bo); ϕ; γ; and the presence of pre-existing plugs initially blocking either daughter tube. A critical capillary number (Cac) was found to exist below which no liquid entered the upper daughter (Rs=0), and above which Rs increased and leveled off with Cap. Cac increased while Rs decreased with increasing ϕ, γ, and Bo for blocked and unblocked cases at a given Cap>Cac. Compared to the nonblockage cases, Rs decreased (increased) at a given Cap while Cac increased (decreased) with an upper (lower) liquid blockage. More liquid entered the unblocked daughter with a blockage in one daughter tube, and this effect was larger with larger gravity effect. A simple theoretical model that predicts Rs and Cac is in qualitative agreement with the experiments over a wide range of parameters.

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